I would like to know the reasoning behind the arrangement of output in Mma's Minors[] function. According to the definition (see, e.g., James and James: Mathematics Dictonary) the minor of an element in a determinant is the determinant, of next lower order, obtained by striking out the row and column in which the element lies.

-(a a ) + a a -(a a ) + a a -(a a ) + a a 12 31 11 32 13 31 11 33 13 32 12 33

-(a a ) + a a -(a a ) + a a -(a a ) + a a 22 31 21 32 23 31 21 33 23 32 22 33

OK, I got all the minors, but at position [[1, 1]], I have the minor associated with a33, not that associated with a11. Call the minors derived according to the definition mij, i.e., mij is the minor obtained by striking out row i and column j, then, the Mma resullt of Minors[] has the structure

Why was this done? I recently had to deal with the determinants of 4x4 symbolic matrices, which I found could be simplified significantly after row- or column-expanding them appropriately. It would have been real nice to use the Minors[] function, if only it would return the sub-determinants in the expected positions!